1. Field of the Invention
The present invention relates generally to scanning probe microscopy (SPM), and more specifically to systems and methods for deconvoluting the effects of surface topography from the effects due to the other physical properties of the surface being scanned.
2. Background of the Invention
U.S. Pat. Nos. 6,095,679, 6,260,997 and 6,405,137 and U.S. patent application Ser. No. 09/584,396 filed Jun. 1, 2000, are incorporated herein by reference in their entirety. These patents and this patent application describe thermal scanning probe microscopes, in which the thermal properties of a sample can be imaged by scanning a thermal probe over the surface of the sample, and methods for obtaining images representative of the thermal properties of the sample. Further background information describing the state of the art is disclosed in the article, “New Adventures in Thermal Analysis,” by D. M. Price, M. Reading, A. Hammiche and H. M. Pollock, Journal of Thermal Analysis and Calorimetry, Vol. 60 (2000) (the “New Adventures” article), which is also incorporated by reference herein in its entirety. The New Adventures article describes the combination of scanning probe microscopes (also referred to as atomic force microscopes ) with thermal analysis material characterization techniques to obtain images of a surface of a sample according to variations in the sample's thermal conductivity or thermal expansivity.
FIG. 1(a) is a schematic diagram of a scanning probe or atomic force microscope. FIG. 1(a) shows a sample 10 having a non-smooth surface 11. A probe tip 12 is held against surface 11 by a cantilever 13 extending from a support 14. A laser 15 directs a laser beam 16 at a mirror 17 attached to the end of the cantilever above the probe tip. The beam reflects from the mirror onto a detector 18. The position of the reflected beam on detector 18 (e.g., areas 1 and 2 on detector 18) is used as a measure of the vertical position of probe tip 12, and hence as a measure of the surface topography of the sample. Probe tip 12 is scanned across the sample in an x-y array as the vertical position is measured, thus providing data for computing a topographical image of the sample surface.
If the material is to be characterized according to its thermal conductivity, the probe tip of a conventional atomic force microscope is replaced by, for example, an ultra miniature resistive heater that also serves as a temperature sensor. Such a probe is illustrated schematically in FIG. 1(b). As shown in FIG. 1(b), preferably the probe comprises Wollaston wires 21 extending from a ceramic insulator 22. This probe can be fabricated, for example, from Wollaston process wire which consists of a thin platinum core (e.g., about 5 microns in diameter) surrounded by a thick silver sheath (e.g., about 75 microns in diameter). The wire is formed into a loop and attached to a support structure to produce a cantilever. The silver at the end of the loop is etched away, exposing a platinum core. The platinum core is a fine platinum filament 23 that is bent down to form a probe tip 24.
When current is passed through the probe, heating occurs primarily in the exposed platinum filament 23. A small silicon wafer cemented across the arms of the Wollaston wire cantilever next to the bent platinum filament 23 is used as the mirror 17 that provides position information via an optical feedback circuit, as described above. The heat lost from the probe is monitored by operating the probe in a constant temperature mode, whereby the power required to maintain the tip at a predetermined constant temperature is measured during data acquisition. Image contrast is obtained because regions of high apparent thermal conductivity require greater power to maintain the probe at the predetermined constant temperature compared to regions of lower apparent thermal conductivity. An alternative is to supply the tip with a constant current and the changes in temperature of the tip can provide equivalent maps of thermal properties.
If the material is to be characterized according to its thermal expansivity, the same probe is used, and the z-axis deflection of the probe is monitored as a function of the probe temperature, while the probe temperature is ramped as in conventional thermal analysis. Also, simultaneous calorimetric information regarding the nature of transitions in the sample can be obtained by measuring the power required to make the probe follow a given temperature program and simultaneously measuring and comparing to the power required to make a reference probe isolated from the sample (e.g., on a reference material) follow the same temperature program, calorimetric information. Alternatively, an AC temperature modulation can be applied during the heating ramp, and the changes in power required to keep the modulation amplitude constant can be measured, thus providing a microscopic analog to modulated temperature differential scanning calorimetry. Although this technique is not currently quantitative, measuring the temperature of a transition is, in many cases, sufficient to identify a phase in the sample.
Another imaging mode can be obtained by localized AC heating of the tip which causes the surface to expand and contract according to its thermal expansivity. This can be detected using a lock-in amplifier to generate an image whose contrast derives from the apparent differences in thermal expansivity of the surface components.
In the above-described cases and as a general rule, in all scanning probe microscopy measurements, the topography of the surface may influence the measurement being made. For example, if the thermal conductivity of a sample is being mapped, when the tip of the probe descends into a depression on the surface, the area of contact between the tip and the sample increases, resulting in an apparent increase in the local thermal conductivity. The opposite is true when the probe meets an asperity.
FIG. 2 illustrates the effect of topography on the apparent thermal conductivity of a sample. The schematic drawings on the left of FIG. 2 represent the surface topography of the sample, and its thermal conductivity (the dark gray represents the higher conductivity phase and the light gray represents the lower conductivity phase). The plots on the right of FIG. 2 illustrate the apparent thermal conductivity of the sample, as it would be measured using prior art techniques. As can be seen, whereas the plots corresponding to the smooth surfaces (plots 1 and 3) accurately represent the thermal conductivities of the sample, the plots corresponding to the rough samples (plots 2 and 4) show a false peak (due to the depression on the left side of the sample) and a false valley (due to an asperity on the right side of the sample). Clearly the effects of topography complicates the interpretation of the thermal image because the information actually being sought is the disposition of the phases having different thermal conductivities within the sample.
The images obtained using the thermal scanning probe microscope can be further enhanced by fitting Gaussian peaks to the distribution of pixel intensity in the histograms. This technique is described in the article “Microthermal Characterization of Segmented Polyurethane Elastomers and a Polystyrene—Poly(methyl methacryalate) Polymer Blend Using Variable Temperature Pulsed Force Mode Atomic Force Microscopy,” D. B. Grandy, D. J. Hourston, D. M. Price, M. Reading, G. Goulart Silva, M. Song and P. A. Sykes (published in Macromolecules 2000, 33, 9348-9359), which is incorporated by reference herein. Briefly, the technique comprises (1) obtaining a thermal scanning microscope image; (2) deriving a histogram distribution of the number of pixels vs. intensity for the image; (3) noting that the histogram appears to show two or more peaks; (4) fitting Gaussian distributions to the peaks in the histogram; and (5) using the intersection between the fitted peaks as a “decision boundary” to re-color the original image.
This process is illustrated in FIGS. 3(a) to (3(c). FIG. 3(a) shows a thermal image of a paracetamol tablet. A linear gray scale between 1.55 mW and 2.075 mW is used to denote the z-axis. FIG. 3(b) is a histogram of the distributions of pixels versus intensity for the image of FIG. 3(a). The raw data shows that there are two peaks in the histogram, one relatively narrow peak a little above 1.625 mW, and a broader peak centered roughly at 1.775 mW. This data has been fitted to two Gaussian distributions, shown in FIG. 3(b) as gray lines. (The narrow peak corresponds to the drug phase, and the broader peak corresponds to an excipient.) The intersection between the two peaks occurs at 1.667 mW. Thus 1.667 mW is the “decision boundary” as to whether a pixel should be assigned to one phase or the other. FIG. 3(c) is a black and white version of the image of FIG. 3(a), obtained by assigning black to all pixels having a value below 1.667 mW, and white to all pixels having a value above 1.667 mW. FIG. 3(c) shows the distribution of the two phases more clearly than does FIG. 3(a).
A more sophisticated approach assigns a probability of the pixel belong to one state or the other. In that case, instead of having purely black or purely white pixels, the pixels are assigned a color on a gray scale ranging from white to black. For example, the gray scale level plot shown in FIG. 4(a) can be used to assign the pixels of the image of FIG. 3(a) to a gray scale level that depends on the probability of the pixel belonging to one phase or the other. FIG. 4(b) shows the result of this approach. The image in FIG. 4(b) is not as dramatic as the image of FIG. 3(c), but is probably more realistic. For example, the gray areas might represent pixels having contributions from both phases, possibly due to the subsurface structure of the sample.